This is a short exact sequence of \((K,H)\) -bicomodule left \(A\) -modules. Utilizing
the 2-cocycle deformation functor from [1]} or
[2]}, we obtain a short exact sequence of
\((K,H)\) -bicomodule left \(A_\theta \) -modules
\({0 [r] & \big (A \,\Gamma ^1(B)\, A\big )_\theta [r]& \Gamma ^1(A)^{~}_\theta [r]^-{\mathrm {ver}} & \big (A\otimes H^{+}\big )_\theta [r] & 0.}\) 
